WASHINGTON — The Obama administration said Friday that it would give people eight more days, until Dec. 23, to sign up for health insurance coverage that takes effect on Jan. 1 under the new health care law.

Julie Bataille, a spokeswoman for the federal Centers for Medicare and Medicaid Services, said the government recognized that consumers might need more time to compare and select health insurance plans because of technical problems that have plagued the online federal insurance marketplace since it opened on Oct. 1.

The administration also said it would delay the 2015 insurance enrollment period for the Affordable Care Act by a month, pushing it beyond the 2014 elections.

The decision means that people who have not signed up for insurance by the end of March will generally have to wait until Nov. 15, 2014, to apply. The second enrollment period was previously scheduled to begin on Oct. 15, 2014.

Jeffrey D. Zients, President Obama’s troubleshooter on the federal exchange repair effort, said Friday that the performance of the website, as measured by response times and error rates, was improving. But he and Ms. Bataille were unable to say how many people were now enrolling.

Enrollment started slowly last month, with just over 106,000 people picking private plans through the federal and state insurance marketplaces. The administration has said it expects seven million people to sign up for such plans by the end of the six-month open enrollment period on March 31.

The original deadline required people to sign up by Dec. 15 for coverage beginning in January. Though the new deadline for such coverage is Dec. 23, Ms. Bataille said that consumers would have until Dec. 31 to pay their share of premiums for the first month.

Insurers and Obama administration officials said they expected to see a large number of people sign up in December, meaning that the government and insurers may need to process a lot of applications in a short time. Whether the federal website, HealthCare.gov, can handle the demand is unclear.

Mr. Zients said that the website could now handle 25,000 users at the same time and would be able to handle 50,000 by the end of this month. At times, he predicted, the demand “will exceed this capacity.” At those times, he said, consumers can queue up to use the website, or they can ask the government to send them “email notifications when it’s a better time to come back to the site.”

When the website went live Oct. 1, officials at the White House and the Health and Human Services Department knew of tests showing it could not handle more than 2,000 users at once, according to emails released this week by the House Committee on Energy and Commerce.

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The House Republican leader, Representative Eric Cantor of Virginia, criticized the administration’s decision to delay the start of the next open enrollment period beyond the 2014 elections.

He said Mr. Obama did not want voters to see higher premiums just before they went to the polls. “If Obamacare is so great,” Mr. Cantor asked, “why are Democrats so scared of voters knowing its consequences?”

The administration also said Friday that insurers would get an extra month to set their rates and file applications for health plans to be sold in 2015. The White House press secretary, Jay Carney, said the delay would help insurers evaluate their experience in 2014 and use it to set rates for 2015. “This gives them more time to assess the pool of people who are getting insurance through the marketplaces and make decisions about what rates will look like in the coming year,” he said.

The Commonwealth Fund, a foundation that specializes in health policy, said Friday that the pace of enrollment was picking up, based on data reported by state exchanges.

“The latest enrollment figures from the 14 states that are running their own marketplaces show that enrollment has climbed to at least 200,000 people nationwide,” said Sara R. Collins, a vice president of the fund.

So far, she said, states report that 173,268 people have signed up in their exchanges, and the Obama administration said last week that 26,794 people had selected plans in the federal exchange.

In a manual describing the enrollment process for states using the federal exchange, the Obama administration says that a consumer is not formally enrolled in a health plan until the insurer receives payment of the first month’s premium. Insurers must begin coverage on Jan. 1 for consumers who have paid their share of the initial month’s premium by Dec. 31, the manual says. Likewise, if a consumer signs up by Feb. 15 and pays the premium by Feb. 28, officials said, the insurer must begin coverage on March 1.

The executive director of Hawaii’s exchange, Coral Andrews, announced her resignation on Friday. The state-run exchange has faced problems like those that have plagued the federal insurance website.

Though the Hawaii exchange website was to open on Oct. 1, software problems kept it dark until Oct. 15. As of Nov. 15, only 257 people had enrolled through the Hawaii exchange.

A version of this article appears in print on November 23, 2013, on Page A17 of the New York edition with the headline: Extra Time to Sign Up for Health Coverage. Order Reprints|Today's Paper|Subscribe